Answer to Question #351047 in Statistics and Probability for Bob

Question

3. QUESTION:

A bag contains fifteen balls distinguishable only by their colours; ten are blue and five are red. I reach into the bag with both hands and pull out two balls (one with each hand) and record their colours.

(a) What is the random phenomenon?

(b) What is the sample space?

(c) Express the event that the ball in my left hand is red as a subset of the sample space.

Answer 1

(a) The random phenomenon is (or rather the phenomena are) the colours of the two balls.

(b) The sample space is the set of all possible colours for the two balls, which is

$$\{(B,B), (B,R), (R,B), (R,R)\}$$

(c) The event is the subset

$$\{(R,B), (R,R)\}$$